The probability of the sample having a mean gas mileage between 27 and 29 miles per gallon will be 0.0116.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
In 2014, new cars had an average fuel efficiency of 27.9 miles per gallon with a standard deviation of 6.8 miles per gallon. a sample of 30 new cars is taken.
Then the probability the sample has a mean gas mileage between 27 and 29 miles per gallon will be
The value of the z-score at x = 27, we have
[tex]z = \dfrac{27 - 27.9}{6.8}\\\\z = -0.13[/tex]
The value of the z-score at x = 29, we have
[tex]z = \dfrac{29 - 27.9}{6.8}\\\\z = 0.16[/tex]
Then the probability will be
[tex]\begin{aligned} P(-0.13 < z < 0.16 ) &= P (z < 0.16) - P(z > -0.13) \\\\&= P (z < 0.16) - [ 1 - P(z < -0.13) ]\\\\&= 0.56425 - (1 -0.44735)\\\\&= 0.0116 \end[/tex]
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if f(x) = 7 x - 3 and g(x) = x^2 - 4x - 8 find (f+g)(x)
Answer:
x² + 3x - 11
Step-by-step explanation:
Adding functions: (f + g)(x) is equivalent to f(x) + g(x)
Here, we are given:
f(x) = 7x - 3g(x) = x² - 4x - 8Simplify:
(7x - 3) + (x² - 4x - 8)
7x - 3 + x² - 4x - 8
x² + 3x - 11
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What is the solution to this system of equations? 2x + 2y = 8 and 4x + 3y = 16
Answer:
y=0, x=4
Step-by-step explanation:
2x+2y=8 --- (1)
4x+3y=16 --- (2)
Multiply the coefficient of x in equation (1) across the variables in equation (2), and multiply the coefficients of x in equation (2) across the variables in equation (1).
8x+8y=32 ---- (3)
8x+6y=32 ---- (4)
Subtract equation (3) from (4)
2y=0, y=0/2, y=0.
Substitute the solution for y=0 into equation (1)
2x+2(0)=8
2x=8
x=4
36) A new car dealership celebrated its grand opening by awarding prizes to 10 buyers. Five of
the buyers received a cash prize of $500, and 3 buyers received a cash prize of $1000. Two
buyers received $2500. If one of the buyers receiving a prize is selected at random, what is the
probability that the buyer received $2500?
Answer:
.20
Step-by-step explanation:
please please help me i will give you a ton of points
Answer:
Step-by-step explanation:
(d). V ≈ 3016
S.A. ≈ 2261
Hi i would give brainlist (Which function best models the following table?
Answer:
A is the answer Have a great day
Step-by-step explanation:
Justin earns an annual salary of $48,000, which is paid monthly. This month Justin had the following deductions:
Federal and state income taxes
$650
Social Security and Medicare taxes
$248
Health insurance premiums
$350
Retirement plan contribution 5% of salary
What is Justin's net pay for the month?
Answer:
$2552
Step-by-step explanation:
First you have to find Justin's monthly salary. You do this by dividing his annual salary by 12 months. 48000/12 = 4000 This means Justin makes $4000 each month. Next we have to find what 5% of that is, in order to know how much his retirement plan contribution costs. To do this you divide 4000 by 100 to know how much 1% of his monthly salary is, and then you multiply that by 5 to know how much 5% of his monthly salary is. 4000/100 = 40 40x5 = 200 .We now know his retirement plan contribution each month costs $200. Now we need to know how much to subtract from his monthly salary to get his net pay for the month. We can do this by adding all of his monthly expenses together and then subtracting that total from 4000. 650+248+350+200 = 1448 4000-1448 = 2552 Justin's net pay for the month is $2552
Compare 2 similar cones...
Answer:
3:1.
Step-by-step explanation:
21:7
= 3:1.
..................................
Answer:
..................................
Step-by-step explanation:
Answer:
..................................
Step-by-step explanation:
No clear question so the answer is the question
HELP ASAP WILL MARK AS BRAINLIST IF YOU SOLVE 2 OF THESE QUESTIONS
1. What base 10 number does 257 eight represent
2. A new operation, #, is defined this way: m#n=m^2-mn. Find the value of 7#(3#2).
Answer:
1. 175
2. 28
Step-by-step explanation:
If you're converting from another base, just multiply each digit, then add up the numbers:
ones digit × 8^0,
tens digit × 8^1
hundreds × 8^2
see image.
The second problem gives you a new operation. Follow the rule by squaring the first number and taking away the first×second. Do the parenthesis first!
see image.
If the current age is considered as x, 13 years ago he was x-13 and in 11 years he will be x+11:
Answer:
Therefore, Peter is 21 years old.
Step-by-step explanation:
[tex]\bf{ x+11=\dfrac{(x-13)^2}{2} \ \Longrightarrow \ 2x+22=x^2-26x+169 }[/tex]
[tex]\bf{ 0=x^2-28x+147=(x-21)(x+7) }[/tex]
Donna earns $1,404 per week at her job. However, 19% of her income gets taken out in taxes, and 12% of her income gets taken out and put into her retirement account. Which is a reasonable estimate of the amount Donna is left with each week after the money is deducted?
Answer:
About 969 dollars
Step-by-step explanation:
I kind of did it the long way. I divided $1,404 by 100 and multiplied by 19. Did the same thing with 12. Added the product of those together and subtracted from 1,404.
(1,404÷100)19 + (1,404÷100)12 = 435.24
1,404 - 435.24 = 968.76
Since it was an estimate I rounded it to the nearest whole number and got 969
Hope this helps. There are probably better methods to solve this problem but this was my way.
Which statement about the equation is true?
5(d + 11) = 2(d - 19)
A. The equation has precisely one solution.
B. The equation has precisely two solutions.
c. The equation has infinitely many solutions.
D. The equation has no solutions.
Answer:
The answer is A.
Step-by-step explanation:
If you put it in Desmos Graphing Calculator it will show the one solution is (-31, -100).
please mark brainliest
lets write the possible subset of the following sets and list the proper subset separately
An improper subset of set T contains all the elements of set T and a null element. The improper subset of set T is {2,3}
What is a subset?In mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be identical;
A) Integers are whole numbers (without fractions) that are either positive or negative. If T={x:X is an integer between 1 and 4}, therefore the elements in set T = {2, 3}
B) Since the elements in set T = {2, 3}, then the number of elements in set T = 2
C) The subsets of set T are {}, {2}, {3} and {2,3}
D) Proper subset of set T are subsets of T that is not equal to T. The proper subsets of T are {2} and {3}
An improper subset of set T contains all the elements of set T and a null element. The improper subset of set T is {2,3}
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Ashmita is 63 inches tall. How does her height compare with the other AP Stats students in her class?
Answer:
Using Logic...she is shorter than most children at that level.
Step-by-step explanation:
Ashmita is 63 inches tall which is 5 foot 3. or 5.25 feet
When AP stats starts you should be in Highschool.
Here are the averages of highschool students, in height.
14 years = 5ft 4.5in (163.8 cm) 5ft 2.5in (158.7 cm)
15 years = 5ft 7in (170.1 cm) 5ft 2.9in (159.7 cm)
16 years = 5ft 8.3in (173.4 cm) 5ft 4in (162.5 cm)
17 years = 5ft 9in (175.2 cm) 5ft 4in (162.5 cm)
Determine whether the value of each power is positive or negative.
(-10)
Positive
Negative
(-3)
(-2)
(-1)
(-6)
(-4)
Done
Intro
Answer:
answer in picture
Step-by-step explanation:
3(2x + 5)= 4 (c-3) I know how to solve it but can someone explain it.
Answer:
3x×2c+1
Step-by-step explanation:
6x+15 =4c-12
[tex] \frac{6x + 15}{4c - 12} = \frac{4c - 12}{4c - 12} [/tex]
[tex] \frac{6x + 15}{4c - 12} [/tex]
[tex] \frac{3x + 5}{2c - 4} [/tex]
[tex]3x + 5 \div 2c - 4[/tex]
[tex]3x \times 2c + 5 - 4[/tex]
[tex]3x \times 2c + 1[/tex]
5. Find the area of the figure below:
5 cm
4 cm
2cm
5 cm
Answer:
33 cm^2
Step-by-step explanation:
To find the are of the figure as a whole, find the area of each rectangle individually and then add them together.
The area of a rectangle is [tex]A = bh[/tex], so the area of the small rectangle would be [tex]4*2[/tex], or [tex]8cm^2[/tex].
The area of the larger rectangle would be [tex]5*5[/tex], or [tex]25cm^2[/tex].
So, adding those areas together, we get [tex]33cm^2[/tex] as the area of the whole figure.
Find the length of ST. ST=?
Answer:
ST = 7
Step-by-step explanation:
By the theorem of intersecting secants outside of a circle, we have:[tex]RS(RS +ST) = RQ (RQ+QP)[/tex][tex]\implies 11(11 +ST) = 9 (9+13)[/tex][tex]\implies 11(11 +ST) = 9 *22[/tex][tex]\implies 11 +ST =\frac{ 9 *22}{11}[/tex][tex]\implies 11 +ST =18[/tex][tex]\implies ST =18-11[/tex][tex]\implies\huge\orange{\boxed{ ST =7}}[/tex]Select the graph of the equation below.
y= 3 over 2 x²+4x-2
What’s the next sequence
(-10)-(-6) ( subtracting integers)
Negative when subtracted is counted as positive because negative multiplied with negative gives positive
-10-(-6)
-10+6
-4 answer
Answer:
-4
Step-by-step explanation:
(-10)-(-6)=
-10 + 6=
-4
hope this helps
have a good day
What is the ratio of the volumes of two similar rectangles, if the ratio of their perimeters is 2:9?
Answer:
Step-the base is equal to length * width.
the formula for the volume of a rectangular prism becomes length * width * height.
the ratio of the volume of a three sided figure is the ratio of their corresponding sides cubed.
so if the ratio of their volumes is 125/64, then the ratio of their corresponding sides id 5/4 because 5^3 = 125 and 4^3 = 64.
since the base area is equal to length * widfth, then the ratio of the areas becomes 5^2 / 4^2 which is equal to 25/16.
the ratio of the base area becomes 25/16.
to confirm, use an example:
original prism has dimensions as shown below:
length = 20
width = 40
height = 60
volume = 20 * 40 * 60 = 48000
base area = 20 * 40 = 800
prims that has sides in a ratio of 5/4 to original prism is shown below:
length = 20 * 5/4 = 25
width = 40 * 5/4 = 50
height = 60 * 5/4 = 75
volume = 25 * 50 * 75 = 93750
base area = 25 * 50 = 1250
ratio of the volumes = 93750 / 48000 = 1.953125
ratio of the base areas = 1250 / 800 = 1.5625
125/64 = 1.953125
25/16 = 1.5625
the formulas work.
the ratio of the volume is 125/64
the ratio of the base area is 25/16by-step explanation:
volume = 20 * 40 * 60 = 48000
base area = 20 * 40 = 800
prims that has sides in a ratio of 5/4 to original prism is shown below:
length = 20 * 5/4 = 25
width = 40 * 5/4 = 50
height = 60 * 5/4 = 75
volume = 25 * 50 * 75 = 93750
base area = 25 * 50 = 1250
Brady borrowed $59.99 from his brother
to buy concert tickets. His brother charges
him a weekly simple interest rate of 3.25%.
Brady pays him back in 4 weeks.
Answer:
Pay back $ 67.79 in four weeks
Step-by-step explanation:
He will have to pay INTEREST FO
59.99 x .0325 x 4 = 7.7987
PLUS the 59.99 that he borrowed
= 67.79
Suppose that 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think that it is defective and remove it from the filling line.
a. If a bottle is removed from the filling line, what is the probability that it is defective?
b. If a customer buys a bottle that has not been removed from the filling line, what is the probability that it is defective?
The probability that a bottle on the line is defective and removed is 0.27 and the probability that a bottle on the line is defective and not removed is 0.03
The probability that a bottle on the line is defective?The given parameters are:
P(Defective) = 30%P(Remove) = 0.9P(Not defective and remove) = 0.2The probability that a bottle on the line is removed if defective is:
P = P(Defective) * P(Remove)
This gives
P = 30% * 0.9
Evaluate
P = 0.27
Hence, the probability that a bottle on the line is defective and removed is 0.27
The probability that a bottle not on the line is defective?This probability is represented as:
Defective and Not removed
It is calculated as:
P = P(Defective) * P(Not Remove)
Using the complement rule, the probability that a defective bottle would not be removed is:
P(Not Remove) = 1- P(Remove)
P(Not Remove) = 1 - 0.9 = 0.1
So, we have:
P = 30% * 0.1
Evaluate
P = 0.03
Hence, the probability that a bottle on the line is defective and not removed is 0.03
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The perimeter of a rectangle is given by P = 2(L + B) where L and B are the lengths of the sides. Find P when L= 17 and B = 13.
Answer:
60.
Step-by-step explanation:
P = 2( 17 + 13)
= 2 * 30
= 60
Which statements about the design are true? select three options. each sprinkler head is placed more than 3 feet from the walkway. if two additional sprinkler heads are placed on the lawn, every square foot of the yard would be watered. the total area watered by each sprinkler is approximately 63.6 square feet. the total area watered by all the sprinklers is approximately 254 square feet. if the sprinklers were placed in two straight lines on the yard, they would water a greater amount of the lawn.
The true statements are:
A. Each sprinkler head is placed more than 3 feet from the walkway.C. The total area watered by each sprinkler is approximately 63.6 square feet.D. The total area watered by all the sprinklers is approximately 254 square feet.Calculations and Parameters:Given that:
Sprinkler head = More than one grid box awayEach grid= 3 feetSprinkler distance= 1.5 boxesRadius=?Area=?To find the radius, 3 * 1.5= 4.5 feet.
The area of each circle=
[tex]3.15(4.5)^2 \\= 63.585 \\ 63.6 ft^2.[/tex]
Hence, the statements that are true are options A, C, and D.
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Answer:
It is A C D
Step-by-step explanation:
:) good luck
I need the answer for the what if one
so you would ski down the mountain to the nearest foot is 2556.06ft
What is the probability of getting a number greater than or equal to 5 when rolling a number cube numbered 1 to 6?
A.1/5
B.1/6
C.1/3
D.2/5
Answer:
C. 1/3.
Step-by-step explanation:
There are 2 favourable outcomes:
a 5 or a 6.
So that is 2 numbers out of 6.
Therefore the probability is 2/6
= 1/3.
find the value of x
please help me out here ill do anything
Answer:
let's find the value of x:
4)
10x=6(5)10x=30x=35)
9(x+4)=8(8+10)9x+81=1449x=63x=76)
y^2=2(2+9)y^2=2×11y^2=22y=√(22)y= 4.69 or 4.7I WILL GIVE BRAINLIST HURRY PLS
The box plot shows the total amount of time, in minutes, the students of a class spend reading each day:
What information is provided by the box plot? (3 points)
The mean for the data
The median for the data
The number of students who provided information
The number of students who read for more than 21.5 minutes
Answer:
10000000 Thousand second ........°°°°°°